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复合优化问题的Fenchel对偶

方东辉   

  1. 吉首大学数学与统计学院, 吉首  416000
  • 出版日期:2017-02-25 发布日期:2017-04-01

方东辉. 复合优化问题的Fenchel对偶[J]. 系统科学与数学, 2017, 37(2): 528-536.

FANG Donghui. Study on the Fenchel Dualities for Composite Optimization Problems[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(2): 528-536.

Study on the Fenchel Dualities for Composite Optimization Problems

FANG Donghui   

  1. College of Mathematics and Statistics, Jishou University, Jishou 416000
  • Online:2017-02-25 Published:2017-04-01

利用共轭函数的上图性质, 引入新的约束规范条件, 建立了复合优化问题与其对偶问题之间的强对偶, 稳定强对偶及稳定全对偶成立的等价刻画,推广了前人的相关结论.

By using the epigraph technique, we give some new constraint qualifications, which completely characterize the strong duality, the total duality, the stable strong duality and the stable total duality between the primal problem with its dual problem. The results of the present paper extend the corresponding ones in the previous paper.

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[1] 方东辉,王梦丹. 锥约束复合优化问题的Lagrange对偶[J]. 系统科学与数学, 2017, 37(1): 203-211.
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